The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity

Gourgiotis, PA; Sifnaiou, MD; Georgiadis, HG

dc.contributor.author	Gourgiotis, PA	en
dc.contributor.author	Sifnaiou, MD	en
dc.contributor.author	Georgiadis, HG	en
dc.date.accessioned	2014-03-01T01:34:46Z
dc.date.available	2014-03-01T01:34:46Z
dc.date.issued	2010	en
dc.identifier.issn	0376-9429	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/20850
dc.subject	Asymptotics	en
dc.subject	Dipolar gradient elasticity	en
dc.subject	Knein-Williams technique	en
dc.subject	Micro-mechanics	en
dc.subject	Microstructure	en
dc.subject	Notch	en
dc.subject	Re-entrant corner	en
dc.subject	Toupin-Mindlin theory	en
dc.subject	Wedge	en
dc.subject.classification	Mechanics	en
dc.subject.other	Asymptotics	en
dc.subject.other	Dipolar gradient elasticity	en
dc.subject.other	Mindlin theory	en
dc.subject.other	Notch	en
dc.subject.other	Re-entrant corner	en
dc.subject.other	Wedge	en
dc.subject.other	Williams	en
dc.subject.other	Continuum mechanics	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Elasticity	en
dc.subject.other	Elastohydrodynamics	en
dc.subject.other	Fracture mechanics	en
dc.subject.other	Microstructure	en
dc.subject.other	Ocean structures	en
dc.subject.other	Standards	en
dc.subject.other	Strain energy	en
dc.subject.other	Asymptotic analysis	en
dc.title	The problem of sharp notch in microstructured solids governed by dipolar gradient elasticity	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s10704-010-9523-4	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s10704-010-9523-4	en
heal.language	English	en
heal.publicationDate	2010	en
heal.abstract	In this paper, we deal with the asymptotic problem of a body of infinite extent with a notch (re-entrant corner) under remotely applied plane-strain or anti-plane shear loadings. The problem is formulated within the framework of the Toupin-Mindlin theory of dipolar gradient elasticity. This generalized continuum theory is appropriate to model the response of materials with microstructure. A linear version of the theory results by considering a linear isotropic expression for the strain-energy density that depends on strain- gradient terms, in addition to the standard strain terms appearing in classical elasticity. Through this formulation, a microstructural material constant c is introduced, in addition to the standard Lamé constants (λ, μ). The faces of the notch are considered to be traction-free and a boundary-layer approach is followed. The boundary value problem is attacked with the asymptotic Knein-Williams technique. Our analysis leads to an eigenvalue problem, which, along with the restriction of a bounded strain energy, provides the asymptotic fields. The cases of a crack and a half-space are analyzed in detail as limit cases of the general notch (infinite wedge) problem. The results show significant departure from the predictions of the standard fracture mechanics. © 2010 Springer Science+Business Media B.V.	en
heal.publisher	SPRINGER	en
heal.journalName	International Journal of Fracture	en
dc.identifier.doi	10.1007/s10704-010-9523-4	en
dc.identifier.isi	ISI:000281681200018	en
dc.identifier.volume	166	en
dc.identifier.issue	1-2	en
dc.identifier.spage	179	en
dc.identifier.epage	201	en